In France, government only refers to the ministers. Prime minister is chief of the government, meaning only the other ministers. But the president is the "chef

In France, government only refers to the ministers. Prime minister is chief of the government, meaning only the other ministers. But the president is the "chef d'état", (chief of state), and I guess what you call government, we call it "the state". So, for a French citizen at least, a country's intelligence is not part of the government but part of "the state".